https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:completing-square-quadratics/v/solving-quadratic-equations-by-completing-the-square 2021-06-30T17:32:40Z Completing the square Some quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn't a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn't a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square* Sal Khan video https://cdn.kastatic.org/googleusercontent/21D9W6Ar02QOFUD04nwNqQWkMGs_P0mXTmgQ6OxvZu6ArMLD__sLMOQVPkjmMPeDYXPDmK9lFwncADaVJkrg0XNc Completing the square Some quadratic expressions can be factored as perfect squares. For example, x²+6x+9=(x+3)². However, even if an expression isn't a perfect square, we can turn it into one by adding a constant number. For example, x²+6x+5 isn't a perfect square, but if we add 4 we get (x+3)². This, in essence, is the method of *completing the square* https://cdn.kastatic.org/ka-youtube-converted/bNQY0z76M5A.mp4/bNQY0z76M5A.mp4 846 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/v/completing-the-square-to-solve-quadratic-equations 2021-06-30T17:32:39Z Worked example: completing the square (leading coefficient ≠ 1) Sal solves the equation 4x^2+40x-300=0 by completing the square. Sal Khan video https://cdn.kastatic.org/googleusercontent/Xfk8YyNRDZjqMMWQhG8mMFqvMosMnuSX5E7DZkggk7LKu1ZGRBDLZfiZhpSVpxRs51hLPLREZsIcwiWzWXuVie8 Worked example: completing the square (leading coefficient ≠ 1) Sal solves the equation 4x^2+40x-300=0 by completing the square. https://cdn.kastatic.org/ka-youtube-converted/TV5kDqiJ1Os.mp4/TV5kDqiJ1Os.mp4 344 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:more-on-completing-square/e/completing_the_square_2 2026-06-16T15:55:43.561813682Z Complete the square Solve quadratic equations of the form ax^2+bx+c by completing the square. Tomer Gal exercise https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/v/understanding-equivalent-forms-of-polynomial-functions-to-answer-questions-in-context 2026-06-16T16:34:33.656713573Z Understanding equivalent forms of polynomial functions to answer questions in context Learn how different forms of the same polynomial function can help you answer questions in context. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/f53d33b8-1eff-489f-886e-29d4f28f64d1_1280_720_base.png Understanding equivalent forms of polynomial functions to answer questions in context Learn how different forms of the same polynomial function can help you answer questions in context. https://cdn.kastatic.org/ka-youtube-converted/YL73k-e8Qs4.mp4/YL73k-e8Qs4.mp4 313 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/v/understanding-equivalent-forms-of-rational-functions-to-answer-questions-in-context 2026-06-16T15:55:43.561813682Z Understanding equivalent forms of rational functions to answer questions in context Understanding what different rational forms support finding specific key features. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/a238422f-7796-4928-a929-ae427de001ac_1280_720_base.png Understanding equivalent forms of rational functions to answer questions in context Understanding what different rational forms support finding specific key features. https://cdn.kastatic.org/ka-youtube-converted/Si1TCvVJ-mk.mp4/Si1TCvVJ-mk.mp4 219 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/v/connecting-equivalent-forms-of-rational-functions 2026-06-16T15:55:43.561813682Z Connecting equivalent forms of rational functions Learn how to connect different forms of equivalent rational equations and understand what key features each form provides. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/a7a535d5-e80c-4b2d-b378-e64becd0eee2_1280_720_base.png Connecting equivalent forms of rational functions Learn how to connect different forms of equivalent rational equations and understand what key features each form provides. https://cdn.kastatic.org/ka-youtube-converted/uNFTcN4ZZMo.mp4/uNFTcN4ZZMo.mp4 541 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/e/identify-the-necessary-form-of-a-function-to-answer-questions-in-context 2026-06-16T19:11:42.716495944Z Identify the necessary form of a function to answer questions in context Students will make connections between equivalent forms of polynomial or rational functions and use the features provided to answer questions in context. Courtney Chernin-Hitchings exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:poly-div-by-linear/v/factor-w-poly-div 2025-07-24T16:23:07.42758501Z Factoring using polynomial division This video breaks down the process of dividing polynomials by linear factors. It starts with a given polynomial and a known factor, then uses polynomial division to rewrite the expression as a product of linear factors. video https://cdn.kastatic.org/googleusercontent/G-5Eyea91xHwpZxqAVAqDfCEXTK-fqJyuWq4n7Tb2x9Th6pPLcYhNCUuB6Fi76Hj3fOoPkpvY28Ymo3Gqt7H6qQ Factoring using polynomial division This video breaks down the process of dividing polynomials by linear factors. It starts with a given polynomial and a known factor, then uses polynomial division to rewrite the expression as a product of linear factors. https://cdn.kastatic.org/ka-youtube-converted/I9PiXAbjnMQ.mp4/I9PiXAbjnMQ.mp4 358 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:poly-div-by-linear/v/factor-w-poly-div-missing-term 2022-10-06T23:23:50.639907812Z Factoring using polynomial division: missing term If we know one linear factor of a higher degree polynomial, we can use polynomial division to find other factors of the polynomial. For example, we can use the fact that (x+6) is a factor of (x³+9x²-108) in order to completely factor the polynomial. We just need to be careful because the polynomial has no x-term. video https://cdn.kastatic.org/googleusercontent/nKam51d4XhdAnfbshLySw-Cynf0B-odIJeg1ynlQ9WtP_Y7xBwigtY0WHqA-SOaOtGyXM4PFH14xihoCc3KFg2S2 Factoring using polynomial division: missing term If we know one linear factor of a higher degree polynomial, we can use polynomial division to find other factors of the polynomial. For example, we can use the fact that (x+6) is a factor of (x³+9x²-108) in order to completely factor the polynomial. We just need to be careful because the polynomial has no x-term. https://cdn.kastatic.org/ka-youtube-converted/AkY3DGzrvk8.mp4/AkY3DGzrvk8.mp4 238 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:poly-div-by-linear/e/factor-using-polynomial-division 2025-09-12T02:00:44.915137743Z Factor using polynomial division Factor polynomials completely by using known factors and polynomial division. Tomer Gal exercise https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-div/x2ec2f6f830c9fb89:remainder-theorem/a/polynomial-division-faq 2022-11-24T02:28:55.815015347Z Polynomial division: FAQ Frequently asked questions about polynomial division article https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/v/estimating-an-oblique-asymptote-graphically 2025-08-28T00:00:48.862639845Z Estimating an oblique asymptote graphically Use a rational graph and your knowledge of oblique asymptotes to estimate its equation. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/f466c040-a0a4-483a-9e5a-87eb20961862_1280_720_base.png Estimating an oblique asymptote graphically Use a rational graph and your knowledge of oblique asymptotes to estimate its equation. https://cdn.kastatic.org/ka-youtube-converted/l_Z8UNIshw0.mp4/l_Z8UNIshw0.mp4 109 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/v/finding-oblique-asymptotes-of-a-rational-function 2025-08-28T00:00:48.862639845Z Finding oblique asymptotes of a rational function Use polynomial division to algebraically identify the oblique asymptote of a rational function if it exists. Sal Khan video https://cdn.kastatic.org/ka_thumbnails_cache/41987e7f-b0b4-4db9-b0c8-2a763388b952_1280_720_base.png Finding oblique asymptotes of a rational function Use polynomial division to algebraically identify the oblique asymptote of a rational function if it exists. https://cdn.kastatic.org/ka-youtube-converted/aYRquz4FsKk.mp4/aYRquz4FsKk.mp4 316 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/ap-precalculus/xe322600f784e4778:polynomial-and-rational-functions/xe322600f784e4778:equivalent-representations-of-polynomial-and-rational-expressions/e/analyze-oblique-asymptotes 2026-06-16T15:55:43.561813682Z Analyze oblique asymptotes Identify oblique asymptotes of rational functions in graph, tabular and equation notation. Courtney Chernin-Hitchings exercise https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:binomial/v/binomial-theorem 2021-04-21T12:01:44Z Intro to the Binomial Theorem The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. The larger the power is, the harder it is to expand expressions like this directly. But with the Binomial theorem, the process is relatively fast! Sal Khan video https://cdn.kastatic.org/googleusercontent/kOuY6Y77kqIalsfcglJc-Qd9QbrmjQOc74DS8zlSU9DAFMtyH2rjzDFCS_EEz9sOlKXNrzzti6zXNMfwphMAq3nK Intro to the Binomial Theorem The Binomial theorem tells us how to expand expressions of the form (a+b)ⁿ, for example, (x+y)⁷. The larger the power is, the harder it is to expand expressions like this directly. But with the Binomial theorem, the process is relatively fast! https://cdn.kastatic.org/ka-youtube-converted/iPwrDWQ7hPc.mp4/iPwrDWQ7hPc.mp4 795 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:binomial/v/pascals-triangle-binomial-theorem 2021-04-21T12:01:45Z Pascal's triangle and binomial expansion Sal introduces Pascal's triangle, and shows how we can use it to figure out the coefficients in binomial expansions. Sal Khan video https://cdn.kastatic.org/googleusercontent/lacyi4dbPLQUrYTQAzYXlY-xcQQw2_pc0i3O8SkGe7OQUqSw24MtodY-jRw9RVLNillIxZmNvvqgj552-9WuyVDx Pascal's triangle and binomial expansion Sal introduces Pascal's triangle, and shows how we can use it to figure out the coefficients in binomial expansions. https://cdn.kastatic.org/ka-youtube-converted/v9Evg2tBdRk.mp4/v9Evg2tBdRk.mp4 500 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:binomial/v/coefficient-in-binomial-expansion 2021-04-21T12:01:44Z Expanding binomials Sal expands (3y^2+6x^3)^5 using the binomial theorem and Pascal's triangle. Sal Khan video https://cdn.kastatic.org/googleusercontent/uoGyQvj-n7uQnItpSJdcP4Zskzl_4E_awYSy7vm51dhwb1Nry2jkS52JE_Ta1ykXxoO10ZWuuTlhscI91dcFR-0l_g Expanding binomials Sal expands (3y^2+6x^3)^5 using the binomial theorem and Pascal's triangle. https://cdn.kastatic.org/ka-youtube-converted/ojFuf9RYmzI.mp4/ojFuf9RYmzI.mp4 521 Equivalent representations of polynomial and rational expressions https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:series/x9e81a4f98389efdf:binomial/e/binomial-theorem 2026-06-09T17:40:46.212160686Z Expand binomials Use the binomial theorem in order to expand integer powers of binomial expressions. Sid Patel exercise